A quantum mechanical alternative to the Arrhenius equation in the interpretation of proton spin-lattice relaxation data for the methyl groups in solids

The theory of nuclear spin-lattice relaxation in methyl groups in solids has been a recurring problem in nuclear magnetic resonance (NMR) spectroscopy. The current view is that, except for extreme cases of low torsional barriers where special quantum effects are at stake, the relaxation behaviour of the nuclear spins in methyl groups is controlled by thermally activated classical jumps of the methyl group between its three orientations. The temperature effects on the relaxation rates can be modelled by Arrhenius behaviour of the correlation time of the jump process. The entire variety of relaxation effects in protonated methyl groups have recently been given a consistent quantum mechanical explanation not invoking the jump model regardless of the temperature range. It exploits the damped quantum rotation (DQR) theory originally developed to describe NMR line shape effects for hindered methyl groups. In the DQR model, the incoherent dynamics of the methyl group include two quantum rate (i.e., coherence-damping) processes. For proton relaxation only one of these processes is relevant. In this paper, temperature-dependent proton spin-lattice relaxation data for the methyl groups in polycrystalline methyltriphenyl silane and methyltriphenyl germanium, both deuterated in aromatic positions, are reported and interpreted in terms of the DQR model. A comparison with the conventional approach exploiting the phenomenological Arrhenius equation is made. The present observations provide further indications that incoherent motions of molecular moieties in the condensed phase can retain quantum character over much broader temperature range than is commonly thought.

Unusual effects in variable temperature powder NMR spectra of the methyl group protons in 9,10-dimethyltriptycene-d₁₂

Variable temperature (1)H wide line NMR spectra of polycrystalline 9,10-dimethyltriptycene-d12 deuterated in the aromatic positions were studied. The spectra show different patterns in an unrepeatable dependence on the way of preparation of the powdered samples. Simultaneously, no anomalies were seen in the MAS and CPMAS proton-decoupled room-temperature (13)C spectra as well as in powder X-ray diffraction patterns. The effects observed in the (1)H spectra are tentatively explained in terms of a phenomenological model. For one of the examined samples it afforded a consistent interpretation of the entire series of temperature dependent spectra in terms of structural non uniformity of the solid material studied. Quantum character of the stochastic dynamics of the methyl groups in the investigated compound was confirmed, although these dynamics are close to the classical limit where the familiar random jump model applies.

Spin-lattice relaxation of the methyl group protons in solids revisited: damped quantum rotation approach

Proton spin-lattice relaxation of the methyl group in solids had been one of the most thoroughly addressed theoretical problems in nuclear magnetic resonance (NMR) spectroscopy, considered at different levels of sophistication. For systems with substantial quantum tunneling effects, several quantum mechanical treatments were reported, although in practical applications the quantum models were always augmented with or replaced by the classical jump model. However, the latter has recently proved invalid in the description of NMR line shape effects in variable-temperature spectra of hindered methyl groups, while the competing theory of damped quantum rotation (DQR) was shown to be adequate. In this work, the spin-lattice relaxation issue for the methyl protons is readdressed using the latter theory. The main outcome is that, while the existing formulas for the relaxation rates remain unchanged, the crucial parameter entering them, the correlation time of the relevant random process, need to be reinterpreted. It proves to be the inverse of one of the two quantum-rate constants entering the DQR model, neither of which, when taken separately, can be related to the jump process. It can be identified with one describing the life-time broadening of the tunnel peaks in inelastic neutron scattering (INS) spectra of the methyl groups. Such a relationship between the relaxation and INS effects was reported from another laboratory long ago, but only for the low-temperature limit where thermal population of the excited torsional levels of the methyl group can be neglected. The whole spectrum of cases encountered in practical relaxation studies on protonated methyl groups is addressed for the first time. Preliminary experimental confirmation of this novel approach is reported, based on already published NMR data for a single crystal of methylmalonic acid. The once extensively debated issues of quenching of the coherent tunneling and of the classical limit in the dynamics of the methyl groups are readdressed and presented in a consistent manner.

NMR study of cation dynamics in three crystalline states of 1-butyl-3-methylimidazolium hexafluorophosphate exhibiting crystal polymorphism

We investigate the cation rotational dynamics of a room temperature ionic liquid (RTIL) 1-butyl-3-methylimidazolium hexafluorophosphate ([C(4)mim]PF(6)) in its three crystalline states by (1)H NMR spectroscopy. Spin-lattice and spin-spin relaxation time (T(1) and T(2), respectively) measurements as a function of temperature confirm the presence of three polymorphic crystals of [C(4)mim]PF(6): crystals α, β, and γ, which we previously discovered using Raman spectroscopy and calorimetry. Second moment calculations of (1)H NMR spectra reveal that certain segmental motions of the butyl group in addition to the rapid rotation of the two methyl groups in the cation occur in all the crystals. The trend in the mobility of the segmental motions is γ < β ≤ α, which is consistent with the strength of cation-anion interactions (or crystal packing density) estimated from high-frequency Raman scattering experiments. T(1) measurements demonstrate two types of rotational motions on the nanosecond time scale in all three crystals: fast and slow motions. The three crystals have similar activation energies of 12.5-15.1 kJ mol(-1) for the fast motion, which is assigned to the rotation of the methyl group at the terminal of the butyl group. These observed activation energies were consistent with that estimated by quantum chemical calculations in the gas phase (11.9 kJ mol(-1)). In contrast, the slow motions of crystals α and γ are attributed to different segmental motions of the butyl group and that of crystal β to either a little segmental motion or a certain PF(6)(-) rotational motion. These nanosecond rotational motions obtained from the T(1) measurements do not appear to be affected by crystal packing density because local interactions in the crystalline state rather than packing density govern such nanosecond motions. With respect to the segmental motions, the mobility is likely to change significantly with the conformation of the butyl group. On the basis of these findings, crystal γ, which is the only crystalline phase previously determined using single-crystal X-ray diffraction, is considered to be the most stable phase because of the slowest segmental motions and the strongest cation-anion interactions.

Temperature dependence of quadratic electrooptic and electrostrictive effects in the paraelectric phase of methylammonium alums

The quadratic electrooptic and electrostrictive constants of NH3CH3Al(SO4)2 · 12H2O (MASD) have been measured between room temperature and the ferroelectric phase transition at −96° C. Both effects increase strongly with decreasing temperature. A thermodynamic analysis of the results reveals the dominant influence of electrostriction on all electrooptic properties. The thermal behaviour of the effects is not compatible with a simple order parameter like the polarization P. Therefore we suggest an intrinsic order parameter θ which couples strongly with P. This assumption allows a correct description of the temperature dependence of the electrostrictive constants above the transition temperature. Thus MASD must be classified as an improper ferroelectric crystal. The essential features of the quadratic electrooptic effect found with MASD also occur in other methylammonium alums.

Electrogyration effect in the paraelectric phase of ferroelectric alums

The electrogyration effect of four methylammonium alums and of ammonium iron alum in their paraelectric phase has been measured. In all methylammonium alums the electrogyration constant s 123 obeys the CurieWeiss-law s 123 = s′123 (T− T 0)−1 + s″123 with only small s″123-values compared with s′123. In contrast to the strong increase in these crystals, s 123 diminishes in ammonium iron alum when the transition temperature is approached. Within the framework of the phenomenological theory of improper ferroelectrics in both kinds of compounds, the electrogyration effect can be described by a sum of two terms, one depending on polarization Pand the other on an intrinsic order parameter [unk], different from P. From dispersion behavior in methylammonium iron alum a less important influence of the trivalent cation on phase transition is concluded.

Spin-lattice relaxation study of the methyl proton dynamics in solid 9,10-dimethyltriptycene (DMT)

Proton spin-lattice relaxation studies are performed for powder samples of 9,10-dimethyltriptycene (DMT) and its isotopomer DMT-d(12) in which all the non-methyl protons in the molecule are replaced by deuterons. The relaxation data are interpreted in terms of the conventional relaxation theory based on the random jump model in which the Pauli correlations between the relevant spin and torsional states are discarded. The Arrhenius activation energies, obtained from the relaxation data, 25.3 and 24.8 kJ mol(-1) for DMT and DMT-d(12), respectively, are very high as for the methyl groups. The validity of the jump model in the present case is considered from the perspective of Haupt theory in which the Pauli principle is explicitly invoked. To this purpose, the dynamic quantities entering the Haupt model are reinterpreted in the spirit of the damped quantum rotation (DQR) approach introduced recently for the purpose of NMR lineshape studies of hindered molecular rotators. Theoretical modelling of the relevant methyl group dynamics, based on the DQR theory, was performed. From these calculations it is inferred that direct assessments of the torsional barrier heights, based on the Arrhenius activation energies extracted from relaxation data, should be treated with caution.

The Effect of Low-Temperature Dynamics of the Dimethylammonium Group in [(CH3)2NH2]3Sb2Cl9 on Proton Spin−Lattice Relaxation and Narrowing of the Proton NMR Line

This paper reports the temperature dependence of the relaxation time T1 (55.2 and 90 MHz) and the second moment of the NMR line for protons in a polycrystalline sample of [NH2(CH3)2]3Sb2Cl9 (DMACA). The fundamental aspects of molecular dynamics from quantum tunneling at low temperatures to thermally activated reorientation at elevated temperatures have been studied. The experimentally observed spin-lattice relaxation rate is a consequence of dipolar interactions between the spin pairs inside the methyl group (1/T(1AE) contribution) as well as the spins belonging to neighboring methyl groups and pairs, methyl spin-outer methyl spin (1/T(1EE) contribution). These contributions are considered separately. Two methyl groups in the dimethylammonium (DMA) cations are dynamically inequivalent. The values of the tunnel splitting of separate methyl groups are obtained from the T1 (55.2 MHz) experiment. The tunneling dynamics taking place below the characteristic temperatures 74 and 42 K for separate methyl groups are discussed in terms of the Schrödinger equation. These temperatures point to the one at which thermal energy C(p)T and potential barrier take the same value. It is established that the second moment of the proton NMR line below 74 K up to liquid helium temperature is much lower than the rigid lattice value, which is due to a tunneling stochastic process of the methyl groups.

NMR study of molecular dynamics in selected hydrophilic polymers

The temperature dependencies of the 1H spin-lattice relaxation times T1 and of the proton NMR second moment M2 in the temperature range from about 90 to 420 K were measured for methyl cellulose, hydroxypropyl cellulose and hydroxypropyl methyl cellulose. The proton spin-lattice relaxation measurements reveal two minima due to the C3 reorientation of the methyl groups of the methoxy, methylenemethoxy or propylene oxide groups and the restricted motion of the segment of the polymer chain. The activation energy barriers for these motions were calculated.

NMR study of monomethylammonium cation in (CH3NH3)5Bi2Cl11 ferroelectric polycrystal

Spin-lattice relaxation times T1 and T1p are determined for protons in three polycrystals (CH3NH3)5Bi2Cl11, (CD3NH3)5Bi2Cl11 and (CH3ND3)5Bi2Cl11. The temperature dependencies of the relaxation times obtained for (CH3NH3)5Bi2Cl11 and (CD3NH3)5Bi2Cl11 are interpreted as a result of correlated motions of the three-proton groups of the monomethylammonium cation. The minimum of the T1p relaxation time is explained as a result of the oscillations of the symmetry axis of the whole cation.

A nuclear magnetic resonance study of molecular motion in solid tris (n-propylammonium) enneachlorodiantimonate (III) (n-C3H7NH3)3Sb2Cl9

Proton magnetic resonance second moment and spin-lattice relaxation time were carried out on polycrystalline tris (n-propylammonium) enneachlorodiantimonate (III), (n-C3H7NH3)3Sb2Cl9, in the temperature range of 10-370 K. The second moment measurements show that the structure is not rigid on the NMR scale at 10 K, the lowest temperature studied, and that CH3 and NH3 groups execute rotations about C3 axis. The proton spin-lattice relaxation measurements reveal two minima due to the motions of the amino and methyl groups. Analysis of the relaxation data yields the activation energy barriers of 11.0 kJ mol(-1) and 5.8 kJ mol(-1), respectively, for the NH3 and CH3 groups' motion. NMR data confirm the phase transition at Tc = 232 K, known from different studies.

Proton dynamics in solid noradrenaline hydrochloride

The temperature dependencies of the proton spin-lattice relaxation times and second moment of the 1H nuclear magnetic resonance line have been measured for noradrenaline hydrochloride. Two symmetric minima of T1 are observed. They can be explained in terms of reorientation of the ammonium groups and proton transfer in the hydrogen bond. The activation parameters have been determined.

Molecular motions and phase transitions in solid bis-n-propylammonium pentabromoantimonate

The proton nuclear magnetic resonance (NMR) second moment and spin-lattice relaxation time for polycrystalline bis-n-propylammonium pentabromoantimonate (nPBA) have been measured from 70 to 290 K. The results are interpreted in terms of the CH3 and NH3 group reorientations for which the activation parameters have been determined. A structural phase transition evidenced at about 220 K is found in the polycrystalline sample of nPBA.

Proton dynamics in solid dopamine and noradrenaline hydrochloride

Proton spin-lattice relaxation times (T1) have been measured as a function of temperature for the following catecholamines: dopamine hydrochloride and adrenaline hydrochloride. For both substances a single symmetric minimum of T1 is observed which can be explained as a result of NH3 (dopamine) and CH3 (adrenaline) reorientation around the three-fold axis of the C-N bond. The activation parameters have been determined.

Molecular dynamics of the methylammonium cation in [CH3NH3]5Bi2Cl11

The 1H relaxation times T1 of methylammonium in chlorobismuthate(III) were measured in the temperature range from 50 to 270 K with a SXP 4/100 Bruker pulse spectrometer at 55.2 MHz. It was found that the T1 temperature dependence has three minima. The individual relaxation rates of the three-proton groups can be described by the O'Reilly and Tsang formula. The results obtained from the fitting procedure, using the typical Woessner formula for complex compounds, allow to conclude that the low-temperature minimum is due to the relaxation of all CH3 groups and the other two minima are due to the relaxation of two and four NH3 groups, respectively. This assignment is based on the X-ray results showing that methylammonium cations are differently bonded in this crystal.